In this specific case, it's quite possible that the gate agent, being a costumer service worker, didn't want a fuss. If someone comes to a gate agent with a boarding pass, they're most likely not double-spending the pass, and suggesting otherwise to them would be a quick way to a tweet saying "today I bought a plane ticket, and when I tried boarding I was told I already boarded and they refused to reimburse me, do not fly [airline]". Of course it would have been the "correct" course of action here but as someone who has interacted with The Public, the gate agent did their best.